Semi-classical Boltzmann equation simulation for trapped Fermi gases

The long-time dynamics of an interacting Fermi gas in the semi-classical regime can be efficiently studied via a numerical simulation of the Boltzmann equation. The simulation can quantitatively model a variety of experimentally relevant setups, including different trapping potentials, driving forces and other perturbations, and a wide range of temperatures and interaction strengths. It is possible to follow the exact trajectories of all particles and hence to extract time-resolved density or momentum profiles, collision profiles, collective modes, etc. In this setup, particle propagation is treated classically, but collisions between pairs of particles are evaluated using the correct s-wave scattering cross section. To also account for Fermi-Dirac statistics, certain collisions must be excluded based on the corresponding Pauli blocking probability. This step is computationally expensive and requires a careful choice of auxiliary parameters. In this talk, I will introduce the general numerical setup and discuss implementations and tests across trap geometries, focusing on the validity of the Pauli blocking procedure.